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Proof step 23 from proof acyclic-rem-not-reachable (previous step)

¬ r0 ∈ ce.nxt ' + x1 + H[r0].nxt ', ce.nxt = H[H[r0].nxt].nxt, path(r ' + x0 + r0 ' + (ce.nxt ' + x1) + H[r0].nxt ', H[r0, ce]), r0 ∈ H, path(ce.nxt ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, reachable(r, r0, H), ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = ce.nxt, r = ce.nxt, r0 = ce.nxt, r0 = null, H[r0].nxt = r0, r = r0, r = H[r0].nxt, H[r0].nxt = null, dups(x1), dups(x0), dups(x0 + x1), ce.nxt ∈ x1, ce.nxt ∈ x0, r0 ∈ x0, H[r0].nxt ∈ x1, H[r0].nxt ∈ x0, r ∈ x1, r ∈ x0, r0 ∈ x1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x0 + r0 ' + (ce.nxt ' + x1) + H[r0].nxt ', H[r0, ce]), r0 ∈ H, path(ce.nxt ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, reachable(r, r0, H), ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ H[r0].nxt = ce.nxt, r = ce.nxt, r0 = ce.nxt, r0 = null, H[r0].nxt = r0, r = r0, r = H[r0].nxt, H[r0].nxt = null, dups(x1), dups(x0), dups(x0 + x1), ce.nxt ∈ x1, ce.nxt ∈ x0, r0 ∈ x0, H[r0].nxt ∈ x1, H[r0].nxt ∈ x0, r ∈ x1, r ∈ x0, r0 ∈ x1

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%in-17: ⊦ r ∈ r0 ' ↔ r = r0; from specification list[reflist]%in-append: ⊦ r ∈ x0 + x1 ↔ ¬ ¬(r ∈ x0 ∨ r ∈ x1); from specification list[reflist]%in-01: ⊦ r ≠ r0 → (r ∈ r0 ' + x0 ↔ r ∈ x0); from specification list[reflist]